Timescale analysis for nonlinear dynamical systems

Insight into the behavior and simplified control of a nonlinear dynamical system can be gained by analyzing the timescale structure. Near an equilibrium point, the eigenvalues and eigenvectors for the linearized system provide the necessary information. Nonlinear systems often operate on multiple timescales away from equilibrium, but there has been no general systematic approach to determine these timescales and the associated geometric structure of the state space. A timescale analysis method based on Lyapunov exponents and vectors is synthesized, and its theoretical basis is established. As an initial demonstration the method is applied to an example system, for which the timescale structure is known by other means, and is shown to yield the correct results.